Hey Thanks so much for the quick response. That code did not actually remove the line extending from the bottom of the slider. What did work is:
DIV#av_section_1.avia-section.main_color.avia-section-default.avia-no-shadow.avia-builder-el-1.el_after_av_layerslider.avia-builder-el-last.container_wrap.fullsize
{
border:0;
}

God knows that couldn’t be the most efficient selector but it does the trick. It’s perfect in Safari and Chrome, but in Firefox a very faint line persists.